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October  2016, 12(4): 1311-1322. doi: 10.3934/jimo.2016.12.1311

Revenue congestion: An application of data envelopment analysis

Habibe Zare Haghighi 1, , Sajad Adeli 2, , Farhad Hosseinzadeh Lotfi 3, and  Gholam Reza Jahanshahloo 3,

1. 

Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
2. 

Department of Financial Engineering, Faculty of Engineering, University of Science and Culture, Tehran, Iran
3. 

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran, Iran

Received  November 2013 Revised  October 2015 Published  January 2016

Congestion is generally used in the economics and indicates a situation where a decrease (increase) in one or more inputs can increase (decrease) one or more outputs. In this paper, we introduce a new concept using data envelopment analysis, and call it revenue congestion. The new concept implies a situation where reduction in some inputs may result in an increase in revenue. This improvement in revenue is rather possible by a simultaneous increase and decrease in outputs due to a reduction in inputs. Then, we try to propose a method to distinguish the revenue congestion and identify its sources and amounts. To illustrate the use of the proposed method, an empirical application corresponding to 30 Iranian bank branches is provided. 16 branches evidence revenue congestion via the proposed approach. This identification is very significant because these branches can increase the revenue of their outputs by eliminating the amounts of revenue congestion in each of their inputs. Moreover, it is found that an increase in all outputs is not always profitable, but rather in some cases a decrease in some outputs and an increase in some other outputs can help the firms to make more profits.
Keywords: Data envelopment analysis, revenue efficiency, congestion, output price, bank branches..
Mathematics Subject Classification: Primary: 90B50, 91B06; Secondary: 90C9.
Citation: Habibe Zare Haghighi, Sajad Adeli, Farhad Hosseinzadeh Lotfi, Gholam Reza Jahanshahloo. Revenue congestion: An application of data envelopment analysis. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1311-1322. doi: 10.3934/jimo.2016.12.1311
References:
[1]

G. R. Amin and M. Toloo, Finding the most efficient DMUs in DEA: An improved integrated model, Computers and Industrial Engineering, 52 (2007), 71-77. doi: 10.1016/j.cie.2006.10.003.

[2]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA, European Journal of Operational Research, 231 (2013), 443-451. doi: 10.1016/j.ejor.2013.05.047.

[3]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Measuring and decomposing firm's revenue and cost efficiency: The Russell measures revisited, International Journal of Production Economics, 165 (2015), 19-28. doi: 10.1016/j.ijpe.2015.03.018.

[4]

P. L. Brocket, W. W. Cooper, H. C. Shin and Y. Wang, Inefficiency and congestion in Chinese production before and after the 1978 economic reforms, Socio-Economic Planning Sciences, 32 (1998), 1-20. doi: 10.1016/S0038-0121(97)00020-7.

[5]

W. Cook, Y. Roll and A. Kazakov, A DEA model for measuring the relative efficiencies of highway maintenance patrols, Information Systems and Operational Research, 28 (1990), 113-124.

[6]

W. W. Cooper, R. G. Thompson and R. M. Thrall, Intoduction: Extensions and new developments in DEA, Annals of Operations Research, 66 (1996), 3-45. doi: 10.1007/BF02125451.

[7]

W. W. Cooper, L. M. Seiford and J. Zhu, A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA, Socio-Economic Planning Sciences, 34 (2000), 1-25. doi: 10.1016/S0038-0121(99)00010-5.

[8]

W. W. Cooper, B. Gu and S. Li, Comparisons and evaluations of alternative approaches to the treatment of congestion in DEA, European Journal of Operational Research, 132 (2001), 62-74. doi: 10.1016/S0377-2217(00)00113-2.

[9]

G. Debreu, The coefficient of resource utilization, Econometrica, 19 (1951), 273-292.

[10]

R. Färe and L. Svensson, Congestion of production factors, Econometrica, 48 (1980), 1745-1753. http://www.jstor.org/stable/1911932?seq=1#page_scan_tab_contents

[11]

R. Färe and S. Grosskopf, Measuring congestion in production, Zeitschrift für Nationalökonomie, 43 (1983), 257-271. doi: 10.1007/BF01283574.

[12]

R. Färe, S. Grosskopf and C. A. K. Lovell, The Measurement of Efficiency of Production, Boston: Kluwer Nijhoff, 1985. http://www.springer.com/gp/book/9780898381559#otherversion=9789401577212

[13]

M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society, Series A (General), 120 (1957), 253-290. doi: 10.2307/2343100.

[14]

G. R. Jahanshahloo and M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion considering textile industry of China, Applied Mathematics and computation, 151 (2004), 263-273. doi: 10.1016/S0096-3003(03)00337-0.

[15]

G. R. Jahanshahloo, F. Hosseinzadeh Lotfi and M. Moradi, A DEA approach for fair allocation of common revenue, Applied Mathematics and Computation, 160 (2005), 719-724. doi: 10.1016/j.amc.2003.11.027.

[16]

G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh Lotfi and H. Z. Rezai, A note on some of DEA models and finding efficiency and complete ranking using common Set of weights, Applied Mathematics and computation, 166 (2005), 265-281. doi: 10.1016/j.amc.2004.04.088.

[17]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information: With an application to European commercial banks, European Journal of Operational Research, 134 (2001), 43-58. doi: 10.1016/S0377-2217(00)00237-X.

[18]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information, European Journal of Operational Research, 144 (2003), 454-457. doi: 10.1016/S0377-2217(01)00398-8.

[19]

R. Lin, Allocating fixed costs and common revenue via data envelopment analysis, Applied Mathematics and computation, 218 (2011), 3680-3688. doi: 10.1016/j.amc.2011.09.011.

[20]

F. F. Liu and H. H. Peng, Ranking of units on the DEA frontier with common weights, Computers and Opreations Research, 35 (2008), 1624-1637. doi: 10.1016/j.cor.2006.09.006.

[21]

A. A. Noura, F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, S. Fanati Rashidi and B. R. Parker, A new method for measuring congestion in data envelopment analysis, Socio-Economic Planning Sciences, 44 (2010), 240-246. doi: 10.1016/j.seps.2010.06.003.

[22]

Y. Roll, W. Cook and B. Golany, Controlling factor weights in data envelopment analysis, IIE Transactions, 23 (1991), 2-9. doi: 10.1080/07408179108963835.

[23]

B. K. Sahoo, M. Mehdiloozad and K. Tone, Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach, European Journal of Operational Research, 237 (2014), 921-931. doi: 10.1016/j.ejor.2014.02.017.

[24]

Z. Sinuany-Stern and L. Friedman, DEA and discriminant analysis of ratios for ranking units, European Journal of Operational Research, 111 (1998), 470-478. doi: 10.1016/S0377-2217(97)00313-5.

[25]

T. Sueyoshi and K. Sekitani, DEA congestion and returns to scale under an occurrence of multiple optimal projections, European Journal of Operational Research, 194 (2009), 592-607. doi: 10.1016/j.ejor.2007.12.022.

[26]

K. Tone and B. K. Sahoo, Degree of scale economies and congestion: A unified DEA approach, European Journal of Operational Research, 158 (2004), 755-772. doi: 10.1016/S0377-2217(03)00370-9.

[27]

Q. L. Wei and H. Yan, Congestion and returns to scale in data envelopment analysis, European Journal of Operational Research, 153 (2004), 641-660. doi: 10.1016/S0377-2217(02)00799-3.

[28]

H. Zare-Haghighi, M. Rostamy-Malkhalifeh and G. R. Jahanshahloo, Measurement of congestion in the simultaneous presence of desirable and undesirable outputs, Journal of Applied Mathematics, 2014 (2014), 1-9. doi: 10.1155/2014/512157.

show all references

References:
[1]

G. R. Amin and M. Toloo, Finding the most efficient DMUs in DEA: An improved integrated model, Computers and Industrial Engineering, 52 (2007), 71-77. doi: 10.1016/j.cie.2006.10.003.

[2]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA, European Journal of Operational Research, 231 (2013), 443-451. doi: 10.1016/j.ejor.2013.05.047.

[3]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Measuring and decomposing firm's revenue and cost efficiency: The Russell measures revisited, International Journal of Production Economics, 165 (2015), 19-28. doi: 10.1016/j.ijpe.2015.03.018.

[4]

P. L. Brocket, W. W. Cooper, H. C. Shin and Y. Wang, Inefficiency and congestion in Chinese production before and after the 1978 economic reforms, Socio-Economic Planning Sciences, 32 (1998), 1-20. doi: 10.1016/S0038-0121(97)00020-7.

[5]

W. Cook, Y. Roll and A. Kazakov, A DEA model for measuring the relative efficiencies of highway maintenance patrols, Information Systems and Operational Research, 28 (1990), 113-124.

[6]

W. W. Cooper, R. G. Thompson and R. M. Thrall, Intoduction: Extensions and new developments in DEA, Annals of Operations Research, 66 (1996), 3-45. doi: 10.1007/BF02125451.

[7]

W. W. Cooper, L. M. Seiford and J. Zhu, A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA, Socio-Economic Planning Sciences, 34 (2000), 1-25. doi: 10.1016/S0038-0121(99)00010-5.

[8]

W. W. Cooper, B. Gu and S. Li, Comparisons and evaluations of alternative approaches to the treatment of congestion in DEA, European Journal of Operational Research, 132 (2001), 62-74. doi: 10.1016/S0377-2217(00)00113-2.

[9]

G. Debreu, The coefficient of resource utilization, Econometrica, 19 (1951), 273-292.

[10]

R. Färe and L. Svensson, Congestion of production factors, Econometrica, 48 (1980), 1745-1753. http://www.jstor.org/stable/1911932?seq=1#page_scan_tab_contents

[11]

R. Färe and S. Grosskopf, Measuring congestion in production, Zeitschrift für Nationalökonomie, 43 (1983), 257-271. doi: 10.1007/BF01283574.

[12]

R. Färe, S. Grosskopf and C. A. K. Lovell, The Measurement of Efficiency of Production, Boston: Kluwer Nijhoff, 1985. http://www.springer.com/gp/book/9780898381559#otherversion=9789401577212

[13]

M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society, Series A (General), 120 (1957), 253-290. doi: 10.2307/2343100.

[14]

G. R. Jahanshahloo and M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion considering textile industry of China, Applied Mathematics and computation, 151 (2004), 263-273. doi: 10.1016/S0096-3003(03)00337-0.

[15]

G. R. Jahanshahloo, F. Hosseinzadeh Lotfi and M. Moradi, A DEA approach for fair allocation of common revenue, Applied Mathematics and Computation, 160 (2005), 719-724. doi: 10.1016/j.amc.2003.11.027.

[16]

G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh Lotfi and H. Z. Rezai, A note on some of DEA models and finding efficiency and complete ranking using common Set of weights, Applied Mathematics and computation, 166 (2005), 265-281. doi: 10.1016/j.amc.2004.04.088.

[17]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information: With an application to European commercial banks, European Journal of Operational Research, 134 (2001), 43-58. doi: 10.1016/S0377-2217(00)00237-X.

[18]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information, European Journal of Operational Research, 144 (2003), 454-457. doi: 10.1016/S0377-2217(01)00398-8.

[19]

R. Lin, Allocating fixed costs and common revenue via data envelopment analysis, Applied Mathematics and computation, 218 (2011), 3680-3688. doi: 10.1016/j.amc.2011.09.011.

[20]

F. F. Liu and H. H. Peng, Ranking of units on the DEA frontier with common weights, Computers and Opreations Research, 35 (2008), 1624-1637. doi: 10.1016/j.cor.2006.09.006.

[21]

A. A. Noura, F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, S. Fanati Rashidi and B. R. Parker, A new method for measuring congestion in data envelopment analysis, Socio-Economic Planning Sciences, 44 (2010), 240-246. doi: 10.1016/j.seps.2010.06.003.

[22]

Y. Roll, W. Cook and B. Golany, Controlling factor weights in data envelopment analysis, IIE Transactions, 23 (1991), 2-9. doi: 10.1080/07408179108963835.

[23]

B. K. Sahoo, M. Mehdiloozad and K. Tone, Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach, European Journal of Operational Research, 237 (2014), 921-931. doi: 10.1016/j.ejor.2014.02.017.

[24]

Z. Sinuany-Stern and L. Friedman, DEA and discriminant analysis of ratios for ranking units, European Journal of Operational Research, 111 (1998), 470-478. doi: 10.1016/S0377-2217(97)00313-5.

[25]

T. Sueyoshi and K. Sekitani, DEA congestion and returns to scale under an occurrence of multiple optimal projections, European Journal of Operational Research, 194 (2009), 592-607. doi: 10.1016/j.ejor.2007.12.022.

[26]

K. Tone and B. K. Sahoo, Degree of scale economies and congestion: A unified DEA approach, European Journal of Operational Research, 158 (2004), 755-772. doi: 10.1016/S0377-2217(03)00370-9.

[27]

Q. L. Wei and H. Yan, Congestion and returns to scale in data envelopment analysis, European Journal of Operational Research, 153 (2004), 641-660. doi: 10.1016/S0377-2217(02)00799-3.

[28]

H. Zare-Haghighi, M. Rostamy-Malkhalifeh and G. R. Jahanshahloo, Measurement of congestion in the simultaneous presence of desirable and undesirable outputs, Journal of Applied Mathematics, 2014 (2014), 1-9. doi: 10.1155/2014/512157.

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